Fiber optics technology has advanced to such a level that it is now possible to fabricate a product having a transmission loss essentially reduced to the theoretical limit. The transmission bandwidth is an important factor for producing a long fiber that can be used for communications without repearters. Since the transmission bandwidth depends mainly on the distribution of the refractive index across the fiber cross-section, the cross-sectional refractive index distribution must be uniform in the longitudinal direction in order to produce a useful long fiber. Optical fibers are generally produced by a method comprising oxidizing gaseous glass-forming materials (such as SiCl.sub.4, GeCl.sub.4 and POCl.sub.3) with the flame from a burner (usually an oxyhydrogen flame burner) and depositing the resulting soot in a rod shape which is then sintered in an electric furnace until it is vitrified, and spinning the resulting transparent glass preform to form a fiber, as disclosed in Izawa et al., U.S. Pat. No. 4,224,046, Fujiwara et al., U.S. Pat. No. 4,135,901, and Proceedings of the I.E.E.E., Vol. 68, No. 10, 1980, titled "Materials and Processes for Fiber Preform Fabrication - Vapor Phase Axial Deposition" by T. Izawa et al. The soot usually contains a dopant that modifies the refractive index of the glass. Therefore, if the distance between the burner and the deposition face of the preform formed by accumulating the soot in a rod form varies, the distribution of the dopant also changes, causing undesirable variations in the refractive index distribution of the resulting optical fiber. In conventional processes for producing the preform, the above disadvantages have been reduced by passing a monochromatic light beam between the burner and the deposition face of the preform in such a manner that the light contacts the deposition face and pulling up the supporting rod of the preform at a controlled rate while maintaining a constant intensity of transmitted light, or, alternatively, by monitoring the position of the deposition end of the preform with a television camera. However, such conventional processes have drawbacks, in that the flame oxidation is usually carried out in a vessel which is isolated from the outside atmosphere in order to prevent contamination by impurities, and, therefore, as the production period is extended, soot adheres to the inner surface of the observation window, which gradually becomes opaque, whereby the position of the deposition face of the preform becomes difficult to monitor.